The diagram shows a cuboid OABCDEFG with a horizontal base OABC in which OA = 4 cm and AB = 15 cm. The height OD of the cuboid is 2 cm. The point X on AB is such that AX = 5 cm and the point P on DG is such that DP = p cm, where p is a constant. Unit vectors i, j and k are parallel to OA, OC and OD respectively.

(i) Express \(\overrightarrow{XP}\) in terms of \(p\), \(\mathbf{i}\), \(\mathbf{j}\) and \(\mathbf{k}\).

(ii) Find the exact value of \(p\) for which angle \(OXP = 60^\circ\).